Butterfly model of single-polarization fibers

An exact analysis of propagation along practical single-mode single-polarization fibers is difficult and involves extensive numerical analysis. The authors present a simple refractive-index profile-the butterfly profile-which exhibits the key features of single-polarization operation, but possesses exact analytical solutions of the scalar wave equation for its modes, enabling such quantities as fundamental-mode cutoff and birefringence to be readily evaluated. The accuracy of perturbation solutions based on axisymmetric profiles can also be determined. By incorporating stress anisotropy, the relative values of cutoff for the two polarizations of each mode are shown to be in quantitative agreement with measured values for the bow-tie fiber